A159949 Numerator of Hermite(n, 1/24).

1, 1, -287, -863, 247105, 1241281, -354589919, -2499523487, 712353753217, 6471255867265, -1839949672471199, -20477166570194399, 5808483395818564033, 76577571062410406977, -21670384262882293332575, -330431150786521054263839, 93285628864864986142460161

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..428

Formula

From G. C. Greubel, Jul 16 2018: (Start)

a(n) = 12^n * Hermite(n, 1/24).

E.g.f.: exp(x - 144*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/12)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 1/12, -287/144, -863/1728, 247105/20736, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 1/24]] (* Harvey P. Dale, Nov 05 2016 *)
Table[12^n*HermiteH[n, 1/12], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 1/24)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(x - 144*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/12)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018

Crossrefs

Cf. A001021 (denominators).

Sequence in context: A259402 A157997 A063362 * A158252 A236869 A158287

Adjacent sequences: A159946 A159947 A159948 * A159950 A159951 A159952

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved